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The maximum distribution of a Gaussian stochastic process indexed by a local field

Part of: Stochastic processes Real functions: Miscellaneous topics

Published online by Cambridge University Press:  09 April 2009

Steven N. Evans
Steven N. Evans
Affiliation:
Department of Mathematics, University of Virginia, Mathematics-Astronomy Building, Charlottesville, Virginia 22903, U.S.A.
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Abstract

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We consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.

MSC classification

Secondary: 60G15: Gaussian processes 60G10: Stationary processes 26E30: Non-Archimedean analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 69 - 87
Copyright
Copyright © Australian Mathematical Society 1989

References

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